Question

Auto pistons at Yongpin Zhou’s plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

(a) What is the value of x?(b) What is the value of R?(c) What are the UCLx and LCLx using 3σ?(d) What are the UCLR and LCLR using 3σ?(e) If the true diameter mean should be 155 mm and you want this as your center (nominal line, what are the new UCLx andLCLx?